Question

the venn diagram shows sets a, b, c, and the universal set u. shade (a ∪ b) ∩ c on the venn diagram.

Explanation:

Step1: Recall De - Morgan's law

$(A\cup B)'=A'\cap B'$

Step2: Analyze the expression $(A\cup B)'\cap C'$

It means the intersection of the complement of $A\cup B$ and the complement of $C$. First, find the elements that are not in $A\cup B$. The set $A\cup B$ consists of all elements that are in $A$ or in $B$ or in both. So, $(A\cup B)'$ are the elements in the universal set $U$ that are not in $A$ and not in $B$. Then, $C'$ is the set of elements in $U$ that are not in $C$. The intersection $(A\cup B)'\cap C'$ is the set of elements that are neither in $A$ nor in $B$ and also not in $C$.

Step3: Shade the region

Shade the region outside of all three circles $A$, $B$, and $C$ in the Venn - diagram.

Answer:

Shade the region of the universal set $U$ that is outside of circles $A$, $B$, and $C$.